Question

A company is placing an order for boxed lunches for a meeting of its executive board. There are 10 members of the board and each will have one lunch. The company is getting the lunches from a restaurant that has 25 varieties of boxed lunches. (a) How many different ways are there for the company to place the lunch order for the 10 lunches? Note that it is not important who gets what lunch. All that matters is how many of each of the 25 possible varieties are purchased.

Answer 1

I have no god dang oddest

Answer 2

There are 3,268,760 different ways to place the lunch order for the 10 lunches.

Explanation:

Who gets what lunch is not important, that means, the order in which the lunches are organized is not important. So the combinations formula is used to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

In this problem, we have that:

10 lunches from a set of 25. So

`C_(25,10) = (25!)/(10!(25 - 10)!) = 3268760`

There are 3,268,760 different ways to place the lunch order for the 10 lunches.